Let f: R arrow R be a function such that f(x)=(x2+2 x+1/x2+1). Then

Question

Let f: R arrow R be a function such that f(x)=(x2+2 x+1/x2+1). Then (A) f(x) is many-one in (-∞,-1) (B) f(x) is one-one in (-∞, ∞) (C) f(x) is many-one in (1, ∞) (D) f(x) is one-one in [1, ∞) but not in (-∞, ∞)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f1d2bcd95ddbb02d18717183e0371103-.png" /> f(x)=((x+1)2/x2+1)=1+(2 x/x2+1) f(x)=1+(2/x+(1)x)

Q. Let $f : R \to R$ be a function such that $f (x) = \frac{x ^{2} + 2 x + 1}{x ^{2} + 1}$ . Then

$f (x)$ is many-one in $(- \infty, - 1)$

$f (x)$ is one-one in $(- \infty, \infty)$

$f (x)$ is many-one in $(1, \infty)$

$f (x)$ is one-one in $[1, \infty)$ but not in $(- \infty, \infty)$

$f (x) = \frac{( x + 1 ) ^{2}}{x ^{2} + 1} = 1 + \frac{2 x}{x ^{2} + 1}$
$f (x) = 1 + \frac{2}{x + \frac{1}{x}}$

Q. Let f:R→R be a function such that f(x)=x2+1x2+2x+1​. Then

f(x) is many-one in (−∞,−1)

f(x) is one-one in (−∞,∞)

f(x) is many-one in (1,∞)

f(x) is one-one in [1,∞) but not in (−∞,∞)